The IM approach has close connections to fiducial inference [1]}, [2]}, generalized fiducial inference [3]}, structural inference [4]}, Dempster–Shafer theory [5]}, [6]}, [7]}, [8]}, [9]}, and others, including Bayesian inference [10]}, confidence structures [11]}, and other calibrated beliefs frameworks [12]}, [13]}. Its construction proceeds as follows. Step 1 is to associate the observable data and unknown quantity of interest with an unobservable auxiliary variable. This association usually characterizes the distribution of data, given the unknowns, but see below. Step 2 is to predict the unobserved value of the auxiliary variable with a suitable, user-defined random set. Finally, Step 3 is to map this random set to the space where the quantity of interest resides and then combine it with the association at the observed data value. This yields a data-dependent random set whose distribution is used to quantify uncertainty about the unknows, in particular, yielding lower and upper probabilities for any relevant assertions. Easy to arrange properties of the user-defined random set ensure that the inference is valid in a (strong) sense similar to that described in Section REF  above. For the readers' convenience, we present some details in Appendix REF  about IMs for prediction under a parametric statistical model.
